How do you simplify #1- (sin^2 theta/ (1-cos theta))= -cos theta#?

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Answer 1 · 2018-03-28T11:09:48

Please see below.

Here,

#1-((sin^2theta)/(1-costheta))=-costheta#

#LHS=1-(sin^2theta/(1-costheta)xx(1+costheta)/(1+costheta))#

#=1-(sin^2theta(1+costheta))/(1-cos^2theta).....to (1-cos^2theta=sin^2theta)#

#=1-((cancelsin^2theta)(1+costheta))/(cancel(sin^2theta)#

#=1-(1+costheta)#

#=1-1-costheta#

#=-costheta#

#=RHS#

Answer 2 · 2018-03-28T11:10:02

#-cos theta#

Firstly take L.H.S.(left hand side),

i.e. #LHS=1 - (sin^2theta/(1-costheta))#

#=1-[(1-cos^2theta)/(1-costheta)]#

#=1-[(1^2-(costheta)^2)/(1-costheta)]#

#=1-[(((1+costheta))(cancel(1-costheta)))/((cancel(1-costheta)))]#

so after solving it will give,

#=1-(1+costheta)#

#=1-1-costheta#

which will give,

#=-costheta#

#=RHS#

hence proved.